As in PSE, PFE also has requirements regarding the stability of the spatial march. Similar to the spatially periodic analysis [1]}, the spectrum from PFE is composed of the main PSE spectrum (with wavenumbers \(\alpha _{PSE}\) ) and modes related to the inclusion of the harmonics (wavenumbers \(\alpha _{PSE} \pm N \alpha _s\) ). This leads to the appearance of new upstream acoustic modes in the spectrum with wavenumbers
\(\alpha _u = - \omega \sqrt{1-z^2} \pm N \alpha _s.\) 
